Nuprl Lemma : real-subset-metric_wf
∀[P:ℝ ⟶ ℙ]. (real-subset-metric() ∈ metric(x:ℝ × P[x]))
Proof
Definitions occuring in Statement :
real-subset-metric: real-subset-metric(),
metric: metric(X),
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-subset-metric: real-subset-metric(),
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
top: Top
Lemmas referenced :
induced-rmetric_wf,
real_wf,
subtype_rel_self,
pi1_wf_top,
istype-void
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesis,
applyEquality,
hypothesisEquality,
instantiate,
universeEquality,
lambdaEquality_alt,
productElimination,
independent_pairEquality,
isect_memberEquality_alt,
voidElimination,
productIsType,
universeIsType,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType
Latex:
\mforall{}[P:\mBbbR{} {}\mrightarrow{} \mBbbP{}]. (real-subset-metric() \mmember{} metric(x:\mBbbR{} \mtimes{} P[x]))
Date html generated:
2019_10_29-AM-11_05_33
Last ObjectModification:
2019_10_02-AM-09_47_11
Theory : reals
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